Gyro-Groups, Gyro-splittings and Co-homology

皮亚诺连续统的一阶同调群的典范分裂

A canonical splitting of the first homology group of Peano continua

该研究对具有无挠一阶切赫同调的皮亚诺连续统的一阶同调群进行典范分裂，推导其作为$\boldsymbol{R}^3$子空间时的同调结构，还构造了对应其道路连通纤维化的一阶同调余挠商。

Hochschild-Pirashvili homology on suspensions and representations of $Out(F_n)$

We show that the Hochschild-Pirashvili homology on any suspension admits the so called Hodge splitting. For a map between suspensions $f\colon ΣY\to ΣZ$, the induced map in the Hochschild-Pirashvili homology preserves this splitting if $f$ is a suspension. If $f$ is not a suspension, we show that the splitting is preserved only as a filtration. As a special case, we obtain that the Hochschild-Pirashvili homology on wedges of circles produces new representations of $Out(F_n)$ that do not factor in general through $GL(n,Z)$. The obtained representations are naturally filtered in such a way that …

Duality and Local Group Cohomology

Recently, Meierfrankenfeld has published three theorems on the cohomology of a finitary module. They cover the local determination of complete reducibility; the local splitting of group extensions; and the representation of locally split extensions in the double dual. In this note we derive all three by combining a certain duality between homology and cohomology with the continuity of homology.

图的可分离同调与可分离复形

Separable homology of graphs and the separability complex

本文研究了图的可分离同调性质，通过引入可分离复形，证明其连通性与fundamental群生成条件的关系，并展示了该复形的非超几何特性。

关于亏格3超椭圆Torelli群的第二同调

On the second homology of the genus 3 hyperelliptic Torelli group

本文研究了亏格3超椭圆Torelli群的第二同调群，证明了简单Abelian循环与H₁(Σ_3;Z)的正交分裂之间存在双射关系，并证明其线性无关性。

The Casson invariant and the word metric on the Torelli group

We bound the value of the Casson invariant of any integral homology 3-sphere $M$ by a constant times the distance-squared to the identity, measured in any word metric on the Torelli group $\T$, of the element of $\T$ associated to any Heegaard splitting of $M$. We construct examples which show this bound is asymptotically sharp.